The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.
What is the graphical solution to a systems of equationsThe graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.
If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.
In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.
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What is the best description of originality?
nonobvious
special or interesting
convergent
having a low probability, unique
Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.
An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.
Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.
Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.
Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.
In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
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Which of the following new vehicle borrowers is likely to be offered the lowest APR?
A. Tyler who is buying a used vehicle and has a FICO score of 780
B. Daniel who is buying a used vehicle and has a FICO score of 600
C. Stephanie who is buying a new vehicle and has a FICO score of 780
D. Emily who is buying a new vehicle and has a FICO score of 600
Answer: C. Stephanie who is buying a new vehicle and has a FICO score of 780.
Step-by-step explanation: The Annual Percentage Rate (APR) is the interest rate charged on a loan. Lenders consider various factors when determining the APR, including the borrower's credit score and the type of vehicle being financed.
In this scenario, Stephanie has a FICO score of 780, which indicates a strong credit history and responsible financial behavior. Lenders generally view higher credit scores as an indication of lower credit risk. As Stephanie is buying a new vehicle, lenders may consider this a lower-risk loan compared to financing a used vehicle.
Lower credit risk and the lower risk associated with financing a new vehicle are factors that could result in Stephanie being offered a lower APR compared to Tyler (option A), who is buying a used vehicle, and Daniel (option B), who has a lower FICO score of 600.
It's important to note that other factors, such as the lender's policies, market conditions, and individual loan terms, can also influence the APR offered to borrowers.
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The volumes of two similar figures are given. The surface area of the larger figure is given. Find the surface area of the smaller figure.
V= 160 meters cubed
V= 2500 meters cubed
S.A. = 1400 meters squared
Answer:
Since the figures are similar, their corresponding side lengths are proportional.
Let x be the scale factor between the larger and smaller figures. Then, the volume of the larger figure is x^3 times the volume of the smaller figure.
We can set up an equation to solve for x:
2500 = x^3 * 160
Divide both sides by 160:
x^3 = 2500/160
x^3 = 15.625
Take the cube root of both sides:
x = 2.5
So, the scale factor between the larger and smaller figures is 2.5.
Since surface area is proportional to the square of the scale factor, we can set up another equation to solve for the surface area of the smaller figure:
S.A. of smaller figure / S.A. of larger figure = (scale factor of smaller figure)^2 / (scale factor of larger figure)^2
Solving for the surface area of the smaller figure:
S.A. of smaller figure / 1400 = 2.5^2 / 1^2
S.A. of smaller figure / 1400 = 6.25
S.A. of smaller figure = 6.25 * 1400
S.A. of smaller figure = 8750
Therefore, the surface area of the smaller figure is 8750 meters squared.
Step-by-step explanation:
Find the area of the following colored regions.
Step-by-step explanation:
r = 4 m
d = 2 × r
d = 2 × 4
d = 8 m = s
Area of square = s × s
= 8 × 8
= 64 m²
Area of circle = πr²
= 3.14 × 4 × 4
= 50.24²
Area of colored region = A. Square - A. Circle
= 64 - 50.24
= 13.76 m²
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Find the area of the composite figure below.
Answer:
Step-by-step explanation:
185
A truck Can be rented from company A for $60 a day plus $0.30 per mile. Company B charges $40 a day plus $0.70 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for company A a better deal than company B’s?
I've been struggling on this question, could anyone help?
The test Statistic and the critical value is 20.692 and 15.308 respectively.
Given that,
Null and Alternative hypothesis,
Null hypothesis: H₀ = 5.7
and Alternative hypothesis: H₁ < 5.7
∴
Test Statistic =
x² = (n-1)s²/σ², where s is the standard deviation = 4.9 and n sample size = 29,
= 28 × 4.9² / 5.7²
= 20.692
The critical value of the left tailed test at significance level 0.025 and df = 28,
x²(critical) = x²(1-α), (n-1) = x²(0.975, 28)
= 15.308
Hence, the test Statistic and the critical value is 20.692 and 15.308 respectively.
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1. Fill in the balance sheet below with each of Rosa's assets and liabilities. Calculate (add up) her total assets and total liabilities. Then calculate her net worth. (15 points) Cash Assets ($) Checking account Liabilities ($) Student loans Credit card(s) balance(s) Net Worth ($) TOTAL ASSETS - TOTAL LIABILITIES
Answer:
Balance Sheet:
Cash Assets ($)
Checking account: $2,000
Liabilities ($)
Student loans: $10,000
Credit card(s) balance(s): $500
Total Assets: $2,000
Total Liabilities: $10,500
Net Worth: Total Assets - Total Liabilities
Net Worth: $2,000 - $10,500
Net Worth: -$8,500
Therefore, Rosa's total assets are $2,000, her total liabilities are $10,500, and her net worth is -$8,500. This indicates that her liabilities exceed her assets, and she has a negative net worth.
What rational number can you multiply by -7/3 in order to get a product of 1? What is the relationship between these rational numbers? Explain your reasoning .
Answer:
-3/7
Step-by-step explanation:
-7/3 × ? = 1
-7/3 × -3/7 = 1
you see how both the three's and Steven's canceled out resulting in one as the answer. also it has to be a negative 3/7 since two negative signs in multiplication result in a positive sign.
Use (SH)RATEY to graph the given rational function. H(x)=2x/x^2-2x+1
The graph of the rational function is attached in the solution.
Given is a rational function we need to graph it,
h(x) = [tex]\frac{2x}{x^2-2x+1}[/tex]
So,
Finding the coordinates by putting the values of x and finding the corresponding values of h(x), the plot them on the graph and join, the curve obtained will be the graph of the function.
Hence, the graph is attached.
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120 was divided by a particular number, then 7 was taken from the quotient. afterwards, this difference was multiplied by 5. giving a product of 25. find the particular number.
The particular number from the given equation is 10.
Given that, 120 was divided by a particular number.
Let the particular number be x.
Here, 120/x
7 was taken from the quotient
120/x -7
The difference was multiplied by 5.
5(120/x -7)
Giving a product of 25
5(120/x -7)=25
120/x -7=5
120/x=12
120=12x
x=120/12
x=10
Therefore, the particular number from the given equation is 10.
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Two boards are placed end to end to make a walkway. One board is 6 feet 11 inches long, and the other board is 5 feet 7 inches long. How long is the walkway?
Write your answer in feet and inches. Use a number less than 12 for inches.
The walkway is 11 feet 6 inches long.
To find the length of the walkway, we need to add the lengths of the two boards.
The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.
The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.
Now we can add the lengths of the two boards:
6 + 11/12 feet + 5 + 7/12 feet
= 11 + 6/12 feet
=11 + 1/2 feet
Therefore, the walkway is 11 feet 6 inches long.
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Lauren kicks a football. Its height in feet is given by h - _ 16t2 + 56t where t represents the time in seconds after kick. Interpret the coordinates of the vertex in context.
Answer: 49.2 feet
Step-by-step explanation:
The given equation h = -16t^2 + 56t represents the height of a football kicked by Lauren as a function of time t in seconds.
In the context of the problem, the vertex of the parabolic function (-16t^2 + 56t) represents the point at which the football reaches its maximum height. The vertex of a parabola is the point where the function reaches its highest or lowest value, and it is given by the coordinates (h, t) in this case.
Interpreting the coordinates of the vertex in context, the h-coordinate represents the maximum height of the football, while the t-coordinate represents the time at which the football reaches that maximum height. So, if we determine the vertex of the given function, we can interpret the maximum height and the time it occurs.
The formula for the x-coordinate (t) of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by t = -b/2a. Comparing this with the given equation, we can identify that a = -16 and b = 56.
Plugging in the values of a and b into the formula, we get:
t = -56 / (2 * -16)
t = -56 / -32
t = 1.75
So, the t-coordinate of the vertex is 1.75 seconds, which represents the time at which the football reaches its maximum height.
To find the h-coordinate of the vertex, we can substitute the value of t we found (1.75) into the given equation:
h = -16(1.75)^2 + 56(1.75)
h = -16(3.0625) + 98
h = -48.8 + 98
h = 49.2
So, the h-coordinate of the vertex is 49.2, which represents the maximum height of the football in feet.
In conclusion, the coordinates of the vertex (49.2, 1.75) in the given context represent the maximum height (49.2 feet) of the football and the time (1.75 seconds) at which the football reaches its maximum height after being kicked by Lauren.
worth 20 points
A net of a rectangular pyramid is shown in the figure.
A net of a triangular prism with base dimensions of 4 inches by 6 inches. The larger triangular face has a height of 4 inches. The smaller triangular face has a height of 4.6 inches.
What is the surface area of the pyramid?
33.2 in2
66.4 in2
90.4 in2
132.8 in2
Add.
9/-8 + -2/5
Write your answer as a fraction in simplest form
The result of carrying out the addition operation on the given fractions, 9/-8 + -2/5, is -61/40.
Addition of fractionsFrom the question, we are to determine the sum of the given fractions
From the given information,
The fraction are 9/-8 and -2/5
We are to carry out the addition operation on the fractions
The addition operation can be carried out on the fractions as follows:
9/-8 + -2/5
First, find the LCM of 8 and 5
The LCM of 8 and 5 is 40
Then,
We can write that
(-45 + -16)/40
= (-45 - 16)/40
= (-61)/40
= -61/40
Hence, the result of adding the fractions is -61/40
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Eli has 38 in cash and 72 on gift card he says that when he rounds to the nearest 10 tickets he has about a $100 is he correct explain
Eli's statement is incorrect. Since $10 is greater than $5, we cannot round $110 to $100 when rounding to the nearest 10.
To determine if Eli is correct, we need to add the amount of cash he has with the value of his gift card;
$38 + $72 = $110
Since Eli says that he has about a $100 when he rounds to the nearest 10, we need to check whether $110 rounds to $100 or not. To round to the nearest 10, we look at the last digit of the number, which is 0 in this case. If the last digit is 5 or greater, we round up to the next multiple of 10. If the last digit is less than 5, we round down to the previous multiple of 10.
Since the last digit of $110 is 0, we don't need to round up or down. $110 is already a multiple of 10. Therefore, Eli is incorrect in saying that he has about a $100 when he rounds to the nearest 10. He actually has $110.
Alternatively, we can check if $110 is within $5 of $100, which is the threshold for rounding to the nearest 10.
$110 - $100 = $10
Therefore, Eli's statement is incorrect.
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I NEED HELP WITH NUMBER 2
Helppppp
( 15) points
The number is given as follows:
x = -3.
How to obtain the number?The variable representing the number is given as follows:
x.
The product of 3 and the number is given as follows:
3x.
Twenty less than the product of 3 and the number is:
3x - 20.
The entire expression is equivalent to -29, hence the value of x, representing the number, is obtained as follows:
3x - 20 = -29
3x = -9
x = -3.
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Last week, the price of oranges at the farmer's market was $2.00 per pound. This week,
the price has decreased by 20%. What is the price of oranges this week?
The mass of one sample of bacteria, in grams, grows according to the expression 8x + 1 , where x is time in hours from now. Another sample of bacteria grows according to the expression 2x − 5 . How long ago did the two samples have the same mass? What was their mass?
The mass of the sample before one hour is negative 7.
Given that:
Mass of the first sample, m₁ = 8x + 1
Mass of the second sample, m₂ = 2x - 5
In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The number of hours when the mass of the samples is the same. Then we have
m₁ = m₂
8x + 1 = 2x - 5
6x = - 6
x = - 1
The mass of the sample before one hour is calculated as,
m₁ = 8(-1) + 1
m₁ = - 8 + 1
m₁ = - 7
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Which of the following expression are equal to -2.5 . 12
The expression -2/5 . 12 is equivalent to the expression (a) 2 . (-12/5)
Evaluating the expression -2/5 . 12From the question, we have the following parameters that can be used in our computation:
-2/5 . 12
The above statement is a product expression that multiplies the values of -2/5 and 12
So, we have
-2/5 . 12 = -24/5
This is because we are multiplying the factors
Next, we ave
(a) 2 . (-12/5) = -24/5
(a) -2/12 . (1/5) = -2/60
This means that the value of the expression is equivalent to (a) 2 . (-12/5)
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Tessa puts 50 marbles in a bag. The number of marbles of each color is shown in the table
below.
Tessa reaches into the bag and randomly selects one marble. What is the probability that the
marble Tessa selects is green?
50
20
2
2/3
Red
15
NUMBER OF MARBLES
Green
20
Blue
10
Yellow
5
A1/50
B1/20
C2/5
D2/3
____________________________________
Green Marbles: 20Blue Marbles: 10Yellow Marbles: 5Red Marbles: 15Total Marbles: 50= 20 ÷ 50 × 100 = 40% There Is A 40% Chance That Tessa Will Select A Green Marble.____________________________________
We have a right prism whose base is a pentagon. Its height is 10ft. The area of the base is [tex]20ft^{2}[/tex]. Solve for LSA and TSA.
The LSA of prism is 157 square feet.
The TSA of prism is 169.738 square feet
We have,
Height = 10 feet
Area of base = 20 square feet
So, area of pentagonal base = 1/4 √5 (5 + 2√5) a²
20 = 1/4 √5 (5 + 2√5) a²
a = 3.14
Now, LSA of prism
= 5bh
= 5(3.14)(10)
= 157 square feet
and, TSA of prism
= 5 x 2(20)/ 15.7 + 157
= 169.738 square feet
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A table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided.
input 1 2 3 4 n
output 5 2 −1 −4
The linear function is solved and the output is y = -3n + 8
Given data ,
Let the linear function be represented as A
Now , the value of A is
The table of inputs = { 1 , 2 , 3 , 4 , n }
The table of outputs = { 5 , 2 , -1 , -4 , a }
So , the first point is P ( 1 , 5 ) and second point is Q ( 2 , 2 )
Slope m = ( 5 - 2 ) / ( 1 - 2 )
m = -3
And , the equation of line is y - 5 = -3 ( x - 1 )
Adding 5 on both sides , we get
y = -3x + 8
Now , when the input is n , the output is
y = -3n + 8
Hence , the equation is y = -3n + 8
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Help me!!!!!! I have to turn this in in a few min
We know that a general quadratic polynomial of the form
Az² +By+Cz+Dy+E=0
can describe many different conics based on the values of the coefficients A and B
Match the name of each conic section given below with the corresponding criteria
on the values of A and B
Ellipse
Parabola
Circle
The requreid match of each conic section has been shown below.
For a general quadratic polynomial of the form Az² +By+Cz+Dy+E=0
Ellipse: A and B have different signs.
Parabola: A = 0 or B = 0, but not both.
Circle: A and B have the same value, and this value is not zero.
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write the following using rational exponents
4√5
The numerical expression 4√5 in the rational exponents will be [tex]4\cdot \left ( 5 \right)^\frac{1}{2}[/tex].
Given that:
Numerical expression: 4√5
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The expression is also written as,
[tex]\rightarrow 4 \sqrt5\\\\\rightarrow 4 \cdot \left ( 5 \right)^\frac{1}{2}[/tex]
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1. A probability experiment which outputs a single number is a(n) _______________ ________________.
(two words)
2. A discrete random variable can output either a finite or a(n) ______________(countably, uncountably)
infinite number of values.
3. A continuous random variable has its values in one or more __________________. An example is the __________________ distribution whose density function is the horizontal line from X=a to X=b.
4. The _________________ __________________ (two words) of a discrete random variable lists every possible value that the variable can assume and the corresponding probabilities.
5. For a(n) _________________ random variable, a sample is drawn with replacement, or there is a large population size. Successive trials are independent of each other. There is a categorical variable with 2 possible values. The ________________(population, sample) is of a fixed size n.
6. For a ____________________ random variable, a sample is drawn without replacement. Successive trials are dependent on each other. There is a ____________________ (population, sample) of finite size N and a categorical variable with 2 possible values. The sample is of a fixed size _______ (N, n, p, q, r).
7. For each blank, include both the formula and the exact answer; do not use a calculator.
Given a uniform distribution with the sample space [1, 4], the height of its density function is ________________ and it has mean ________________ and standard deviation __________________.
8. The ___________________ ____________________ (two words) distribution has a density function that is bell shaped and symmetric. Its mean is 0 and its standard deviation is 1.
9. The ___________________ is also known as the average, expectation and expected value.
10. The ___________________of a discrete random variable can be found by taking the product of each outcome and its probability and then summing.
11. The ______________________ (one word!) of a discrete random variable can be found by subtracting the square of its mean from the expectation of the square of the random variable.
determine the exact values of x for x^2 - 8x - 5 = 0
The exact values of x for x² - 8x - 5 = 0 are x = 4 + √21 or x = 4 - √21
To solve for x in the equation x² - 8x - 5 = 0, we can use the quadratic formula, which is:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
Using this formula, we can identify the values of a, b, and c in the equation x² - 8x - 5 = 0.
Here, a = 1, b = -8, and c = -5.
Substituting these values into the formula, we get:
x = (-(-8) ± √((-8)² - 4(1)(-5))) / 2(1)
Simplifying this expression, we get:
x = (8 ± √(64 + 20)) / 2
x = (8 ± √84) / 2
Now, we can simplify the square root of 84 as 2√21:
x = (8 ± 2√21) / 2
We can further simplify this expression by factoring out 2 from the numerator:
x = 2(4 ± √21) / 2
Canceling out the 2s, we get:
x = 4 ± √21
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The average monthly income of three persons is rs. 3,600. If the income of the first is 1/5 of the combined income of the other two then his monthly income is
The monthly income of the first person is $600.
Given that, the average monthly income of three persons is RS 3,600.
The income of the first is 1/5 of the combined income of the other two.
Here, Let income of the first be A, let income of the second be B and let Income of the third be C.
A+B+C=3600 -----(i)
Income for the first person = 1/5(B+C) -----(ii)
Substitute equation (ii) in equation (i), we get
(B+C)/5 +B+C =3600
B+C+5B+5C=3600×5
6B+6C=18000
6(B+C)=18000
B+C=3000 ------(iii)
Substitute (iii) in equation (i), we get
A=$600
Therefore, the monthly income of the first person is $600.
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The following data were used in a regression study.
Observation 1 2 3 4 5 6 7 8 9
xi
2 3 4 5 7 7 7 8 9
yi
4 5 4 6 4 6 9 6 11
(a)
Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)
ŷ =
The estimated regression equation for these data is ŷ = 0.69x + 2.15
Developing an estimated regression equation for these dataFrom the question, we have the following parameters that can be used in our computation:
Observation 1 2 3 4 5 6 7 8 9
xi 2 3 4 5 7 7 7 8 9
yi 4 5 4 6 4 6 9 6 11
Using a graphing tool, we have the following calculation summary
Sum of X = 52Sum of Y = 55Mean X = 5.7778Mean Y = 6.1111Sum of squares (SSX) = 45.5556Sum of products (SP) = 31.2222Regression Equation: ŷ = bX + a
Where
b = SP/SSX = 31.22/45.56 = 0.68537
a = MY - bMX = 6.11 - (0.69*5.78) = 2.15122
So, we have
ŷ = 0.68537x + 2.15122
Rounding the numerical values to two decimal places, we have
ŷ = 0.69x + 2.15
Hence, the estimated regression equation for these data is ŷ = 0.69x + 2.15
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